**4. Conclusions**

This study simulated the unsteady conditions of a Hyperloop system using the overset moving mesh to investigate the influences of pod speed, BR, tube pressure, and pod length on the aerodynamic drag and pressure waves induced in the system.

The results provide a clear picture of the variation of the drag coefficient. The drag coefficient is maximized at lower pod speeds with a higher BR, in other words, 225 m/s for BR = 0.36 and 250 m/s for BR = 0.25. The drag coefficient increases with the increase of pod speed, BR, and pod length. In the Hyperloop system, pressure drag is regarded as a considerable component of total drag, whereas the influence of friction drag is minor. In addition, the pressure difference between the nose and the tail significantly impacts the pressure drag, and consequently the total drag. The drag increases proportionally with the tube pressure, whereas the drag coefficient decreases slightly. The increase of total drag with the increase of pod length is mostly dependent on the increment of the friction drag.

The presence of compression waves and expansion waves generates the opposite tendency of pressure in the front and rear of the pod. Once the local flow speed exceeds the supersonic speed, oblique shockwaves occur, vastly influencing the tail pressure of the pod. In the smaller tube (higher BR), the compressed air pushes the pod nose and significantly increases the pressure at the front while decreasing the pressure behind the pod.

The compression waves and expansion waves, along with their speeds were investigated. In the Hyperloop system, these waves become faster than the local speed of sound at lower internal tube pressures and higher operating speeds. As BR increases, the speed of compression wave propagation is largely affected, while the expansion waves propagate at a similar speed. The study also suggested that the normal shockwave theory can be used to predict the variation of compression wave propagation speed.

**Author Contributions:** Conceptualization, methodology, and investigation: T.T.G.L. and J.R.; validation and writing—original draft preparation: T.T.G.L.; formal analysis, data curation, and visualization: T.T.G.L. and K.S.J.; writing—review and editing, supervision, project administration, and funding acquisition: K.-S.L. and J.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2020-2020-0-01655) supervised by the IITP (Institute of Information and Communications Technology Planning and Evaluation), and by the National Research Foundation of Korea (NRF) gran<sup>t</sup> funded by the Korean governmen<sup>t</sup> (MEST) (No. 2019R1A2C1087763). This research was supported by "Core Technology Development of Subsonic Capsule Train" of the Korea Railroad Research Institute under Grant PK2001A1A, Korea.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A. Pressure Wave Propagation with Respect to Simulation Time**

In this study, 1 s was sufficient for the flow to fully develop. Therefore, the tube was created long enough and the pod was placed at the given position to prevent the pressure waves from being reflected by the boundaries in 1 s. The following figures show that at *t* = 1 s, the compression waves and expansion waves do not reflect off the boundaries. Therefore, the designed geometry is reasonable.

**Figure A1.** Pressure line plot along the centerline in the front and rear of the pod varied with simulation time (*vP* = 350 m/s). The simulation was terminated before the expansion wave could reflect off from the outlet boundary.
